[EM] Automatic LIIA Independent of Locking Order

[Kevin Venzke]

 Hi Gustav,

Le vendredi 1 mai 2026 à 08:52:30 UTC−5, Gustav Thorzen via Election-Methods <election-methods at lists.electorama.com> a écrit :
> Ranked Pairs satisfy Local Independence of Irrelevant Alternatives criterion,
> but I got curious if this property is obtained independently of locking order.
> 
> For context, ISDA comes independently of locking order,
> but ISDA is implied by LIIA + Majority criterion,
> so I got curious if LIIA is what actually is obtained
> and ISDA simply followed from it.
> 
> I tried to create a proof for a positive result,
> but quickly discovered I could not figure out how
> to cover scenarios containing multiple matchups
> to be locked in at the same time.
> 
> Any help would be much appreciated.
> Gustav

I've never implemented Ranked Pairs as locking multiple defeats at the same time,
since there could be cyclic incompatibilities introduced by this. Instead I try to
traverse all possible orderings (or agree on a random tiebreaker for pairs ahead of
time). That's not very convenient for proofs, I guess.

> P.S: I have started to suspect I need to fail LIIA
> for a MMPO locking order to satisfy all of
> AFB+Mono+LN-Harm+MB-ISDA
> unless LIIA satisfaction is automatic independently of locking order,
> and then figured it was interesting enough of a question on its own.

Maybe you know this, but the MMPO locking order would normally just give you MAM
itself. The fact that MMPO doesn't normally care about who won or lost each matchup
makes no difference if you try to lock the stronger one first anyway.

I understand of course that you only want to use the majorities, so you won't end up
with a copy of MAM.

I am puzzled that you hold out hope for using a locking order to make a method
satisfying AFB or LNHarm. I feel that from the examples I posted earlier, looking at
the nature of the issues, one sees that the problem is not the specific rule that
orders the defeats, but the wide range of effects from adjusting rankings.

Kevin
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